A method and a concrete mixer of this type are known from practical applications. The consistency is determined by measuring the driving power absorbed by the mixing drum. This is carried out by measuring the driving torque or the hydraulic pressure of a hydraulic motor driving the mixing drum. The drag surface opposing the flow of the concrete and substantially determining the driving torque absorbed by the mixing drum is formed by the interior wall surface of the mixing drum and by installations within the mixing drum, such as mixer blades and the like. During the phase in the course of which the driving power absorbed by the mixing drum is measured, these drag surfaces are only intermittently and/or partially in contact with the concrete. The size of the drag surface is largely dependent on the filling degree of the mixing drum. In addition, the driving torque absorbed by the mixing drum largely depends on whether or not the concrete mixer stands on level ground. Particularly in the case of mobile mixers it is not always possible to ensure that they always stand on level ground at a construction site. Since the consistency of the concrete is adjusted on the base of a comparison of the measured driving torque to a predetermined reference torque, the numerous distorting influences prevent an accurate adjustment of the consistency from being reliably achieved by the known method and with the known concrete mixer, so that the adjustment of the consistency is rather arrived at by chance.